My memory recently lost this so I am relearning. It’s not as easy as it seems. Corrections welcome.
Lay is a transitive verb–something is being done to something else. I lay the child down to sleep. Lie is an intransitive verb–nothing or no one is being acted on. Now I lie down to sleep. The past tense of lay is laid. Last night I laid the child down right after dinner. The past tense of lie is lay. Last night I lay down to sleep soon after midnight. The past participle of lay is laid (same as the past tense). I have laid the child to sleep three times now. The past participle of lie is lain. I could have lain in bed until lunch. Layed is not a word; use laid.